Hello, I need some help with differential equation solving in MATLAB. i got the following equation: (f is a function of two variables: distance x and time t)
df(x,t)/dt = (x - f(x,t))/(f'(x,t)) - x
where f'(x,t) is the derivative of f in respect to x. i wrote the function as: (by multiplying both sides with df/dx)
(df/dt) * (df/dx) = x-f - x*(df/dx)
i am using the MATLAB pdepe function to solve the equation and i keep receiving the following error:
"Warning: Failure at t=3.221102e-001. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.881784e-016) at time t. > In ode15s at 747 In pdepe at 317 In solve at 11
Warning: Time integration has failed. Solution is available at requested time points up to t=3.201601e-001."
Can someone help me??
This is my code:
function [c,f,s] = eqn1(x,t,u,DuDx)
c=DuDx;
f=-x*u;
s=x;
end
function value = initial1(x)
value=0.5*(x^2);
end
function [pl,ql,pr,qr] = bc1(xl,ul,xr,ur,t)
pl=ul;
ql=0;
pr=ur-1;
qr=0;
end
close all; clc; clear all; clc;
m=0;
options=odeset('NonNegative',[]);
x = linspace(0,1,100);
t = linspace(0,20,20*100);
u = pdepe(m,@eqn1,@initial1,@bc1,x,t,options);
surf(x,t,u);
title('Surface plot of solution.');
xlabel('Distance x');
ylabel('Time t');
